I have done everything as per instructions.
Here are my steps:
I went the following path:
Federal Taxes=>Wages & Income=>Business Items=>Schedules K1=>Partnerships
In the section "Describe The Partnership", the following two boxes were checked:
1) "I have passive losses carried over from last year"
2) "All of my investments are at risk"
Then, I went through the following:
Report Carryovers=>Regular Tax=>Box 1
In the "Ordinary Income", I put the loss carried over from the previous year.
Still no form 8582 was generated. There should have have been one generated, as not only was there a carryover from previous year, but also 2021 has a passive loss.
